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C₁₉×#3504 #14561361

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

988 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,25)(22,26,27,24)(28,29)(30,34)(31,38)(32,33)(35,39)(36,42)(37,40)(41,43);(29,33)(34,40)(35,38)(41,42);(20,22,23,27)(21,24,25,26)(28,30,32,37)(29,34,33,40)(31,36,39,43)(35,41,38,42);(28,29)(30,34)(31,35)(32,33)(36,41)(37,40)(38,39)(42,43);(28,31,32,39)(29,35,33,38)(30,36,37,43)(34,41,40,42)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2236);